PREFACE

This book is based on the lecture notes

used by the author for a course entitled "Inter-

mediate Fluid Mechanics" offered for the Senior

and first-year graduate students at Virginia

Polytechnic Institute. It is written with the aim

of acquainting the readers with the fundamental

concepts in analytical fluid mechanics. Theorems

and Formulae are introduced in their general

forms. Selected topics in incompressible inviscid

flow, compressible inviscid flow, viscous flow, turbulence, and magnetohydrodynamics, are then discussed. A limited number of problems are

appended to the end of each chapter. They are

designed to bring out additional fundamental in-

formations in the various disciplines of fluid

mechanics, and should not be thought of as mere exercises. Topics of advanced nature, such as

INTRODUCTION

1.1 Microscopic and Macroscopic Properties of a

Fluid

The most obvious and straight-forward method

of

describing fluid motion is to consider the

kinematics and kinetics of each and every volumetric element of the fluid. If it is assumed that these elements obey the classical or Newton's law of motion, and that for each element there are two distinct types of kinematic motion (ran-

dom and average motion); then by postulating some

statistical distribution of the motions of the

volumetric elements, we can proceed to calculate the motion of the fluid in terms of its average

motion and its local fluctuations. This method

of describing fluid motion has been employed by

the modern scientists in studying the turbulent